How many-body effects modify the van der Waals interaction between graphene sheets

Cold undoped graphene sheets were previously predicted [1,2], via Random Phase approximation (RPA) arguments, to exhibit an unusual asymptotic van der Waals (vdW) interaction energy $E = - KD^{-3}$ where $D$ is the (large) separation between the two parallel graphene sheets. This is compared with $D^{-5/2}$ for 2D metals [3] and $D^{-4}$ for 2D insulators [3]. Here we show [4] that graphene is the first known system where effects beyond the RPA should make QUALITATIVE changes to the vdW force. For large separations, $D>10 nm$ where only $\pi_z$-mediated vdW forces remain, we predict that the vdW interaction is substantially reduced from the RPA prediction, and has a different power law. This new $D$ dependence is very sensitive to the form of the long-wavelength many-body renormalization of the velocity of the massless Dirac fermions, and may provide independent confirmation of the latter. We will briefly discuss issues involved in possible experiments. \\[4pt] [1] J.F. Dobson, A. White and A. Rubio, Phys. Rev. Lett. 96, 073201 (2006).\\[0pt] [2] T. Gould and J. F. Dobson, Phys. Rev. B 87, 165422 (2013).\\[0pt] [3] M. Bostrom and B. E., Sernelius, Phys. Rev. B 61. 2204 (2000).\\[0pt] [4] J.F. Dobson, T. Gould and G. Vignale, ArXiv 1306.4716 (2013).